A conventional wisdom regarding search models is that multiple unemployment equilibrium may result if the matching function has increasing returns to scale. Essays one and two challenge this view in models where projects are homogenous but the job seekers and firms choose their search intensities (essay one), or the job seekers choose their search intensity but firms enter the market according to a zero-profit condition (essay two). Multiple equilibrium may in principle be caused by strategic complementarity or by common pool externality. It turns out that large returns to scale do not endanger uniqueness but rather guarantee it. In directed search models, the identity of stayers and movers has traditionally been just assumed. In essay thr...